BEHOLD my complicated graphic!
Yes, it's that easy! Let me explain. What follows is a synthesis of my personal experience reading and playing these games, as well as from reading various posts from the relevant creators of these games.The original D&D game was closely tied to Chainmail, the rules for miniature mass combat. The core classes were the fighting man, the cleric, the magic-user, the elf, the dwarf, and the halfling (yes, race-as-class). The elf was a unique class, a bit vague in description but most people interpreted the elf to be something of a dual class character (fighting man/magic-user) that only had access to one set of class abilities each day. As many know, these rules were spread among three books. There were many vagaries in descriptions of, well, everything. Partly this is because there was a lot of excitement when the game was being developed, and it ended up going out the door as a rush job. In the current "old-school" climate it will be unpopular to say this, but many or most inconsistencies and vagaries in OD&D are not because it was intentionally left to be house ruled or "imagined the hell out of." That was for the game in general, and yes for rules not covered, but I'm talking about something else. Many of the rules vagaries were simply oversites or failures to anticipate what details would be most needed in play, or by simple error of ommission. This of course is understandable, because the game was revolutionary and treading new ground. By no means am I an OD&D hater, I just think it is appropriate to look at it in its historical context, not the romanticized context many have for it now, which is the only reason I bring it up.
Then the various supplements started coming out. Each one added more complexity to the game, not just in new classes or magic, but in the way attributes affect the game and in the assumptions of "power level." The monsters become more powerful, able to deal more damage.
Then, for reasons that may forever lie in the mists of time and lawsuits, OD&D underwent the "great divide." The rules had become a mess anyway, and reorganization was in order. Couple that with the pending Arneson lawsuit, and it was seen to be desirous to sort of "split" the game, not unlike Danny DeVito and Arnold Schwarzeneggar in the movie "Twins," so that all the genetic garbage went to AD&D, and all that was good and wholesome went to the Moldvay/Cook/Marsh D&D (just kidding!).
So, most of what was seen to be "derived from" original D&D went to Moldvay/Cook/Marsh. Much of the added material from supplements, with the added complexity, went to AD&D.
There never actually was a "basic" D&D, just D&D and AD&D.
What was the result? The main result was that the core OD&D rules went to Moldvay/Cook/Marsh virtually unchanged. The thief class came, too, and the elf was made into a sort of "multiclass" fighter/magic-user. But largely if you ignore the thief and the elf, you have a revised, clarified OD&D in Moldvay D&D.
Meanwhile, AD&D added the greater complexity of separate races and classes, bumped all the HD up so the characters are tougher, and added other detail to monster stats, PC stats, etc. All-in-all, probably the only true mechanical incompatibilities, aside from the greater complexity in general, between D&D and AD&D was that time works a little different in AD&D, and AD&D has a 0-10 AC system instead of the 0-9 system handed to D&D from OD&D.
Yes, this is somewhat simplified, but not too much so. I'm painting with a broad brush. There are people who could list various little details that are different among these additions, but I'd argue that they are largely irrelevant to most people, and those things are not noticed in play. There's a reason so many people never realized D&D and AD&D were "two different games" back in the day, and played by mixing the two. Most people actually played AD&D pretty much as outlined in Moldvay D&D, except with the added classes and races.
These are the essentials of the three-pillar lineage.
